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%I #9 Dec 18 2017 22:49:14
%S 4,43,210,1162,6959,39608,226599,1305725,7497482,43051551,247361324,
%T 1420935204,8162170909,46887717710,269343435641,1547219822419,
%U 8887903925214,51055949141455,293287243303968,1684768052870030
%N Number of n X 3 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.
%C Column 3 of A296688.
%H R. H. Hardin, <a href="/A296683/b296683.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A296683/a296683.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 4*a(n-1) + 4*a(n-2) + 37*a(n-3) - 15*a(n-4) + 21*a(n-5) - 79*a(n-6) - 7*a(n-7) - 92*a(n-8) - 49*a(n-9) - 19*a(n-10) - 20*a(n-11) + 2*a(n-12).
%F Empirical formula verified by _Robert Israel_, Dec 18 2017: see link.
%e Some solutions for n=6:
%e 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1
%e 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0
%e 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1
%e 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0
%e 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0
%Y Cf. A296688.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 18 2017
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